each gestalt are calculated. Steps (16)-(23) apply also to these resulting stalks.
Example. We mention that at the time this paper was written the MeloTopRUBETTE’s graphical interface had not been implemented yet. As consequence we choose for this paper to exhibit only briefly some numerical outputs without commenting their meaning.
In the following the numbers in parentheses refer to the flowchart from Figure 2. We analyse Robert Schumann’s Träumerei (from Kinderszenen). The score is given (00) to our program as a midi file. We select (01) for example the
shape type and the
paradigmatic group for our analysis. The score contains (1) 462 notes which give (2) a total of 355999 motives of 2 to 5 notes within a span of maximal one bar. These motives are classified (4) in 172 gestalts with respect to their shape images (3) and the
group. The minimal (non null) and maximal relative Euclidean distances are (8) respectively 0.283 and 1.265. We evaluate (5, 7, 10-16, 22-23) quantification functions at all radii (9) where neighborhoods vary: there are 30 radii values. For example, the heaviest gestalt (20) at smallest non-null radius
is the gestalt of the motif composed of the first 3 score notes. This motif class contains 16570 representatives. The generic gestalt (5) of the motif composed of the score’s 5 first notes contains 3 gestalts in its topological closure which corresponds to 22563 motives.
5 RUBATO’s MeloTopRUBETTE vs Melo-
RUBETTE
We compare our module, the MeloTopRUBETTE, with its first version the RUBATO MeloRUBETTE. There are many changes, mainly with respect to the outputs. We recall that RUBATO was first designed for experimenting a performance theory. That is why the output of the MeloRUBETTE, simulating a motivic analysis of a score, is meant to serve the performance Rubette. Therefore the unique output of the MeloRUBETTE is the resulting Mazzola note weights: To each note a real number is associated which corresponds to its ’motivic importance’ within the whole score.
Our approach is different: we are interested in the topological model itself, and in its applications, for example in the performance theory. Since the validity of the latter model has not been tested yet, one first important feature is to have an easy access to each step of the program in order to adjust the parameters within the whole model. This is what we propose as major improvement of the MeloTopRUBETTE against the MeloRUBETTE: The interactive control of the ongoing computational process making possible to improve and to extend the model ”on the flight”. In other words, this computational steering approach helps understanding and also modifying the mathematical model on motivic analysis of music. Also, the MeloTopRUBETTE does not hide any part of the topological model, in contrary, it reveals all possible details about the motivic space of a score, which, on the other hand, is completely hidden by the MeloRUBETTE.